Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

• URL: http://arxiv.org/abs/2011.11214v3
• Date: Thu, 17 Jun 2021 09:40:12 GMT
• Title: Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Authors: Marin Bukov, Markus Schmitt, Maxime Dupont
• Abstract summary: We investigate a class of universal variational wave-functions based on artificial neural networks. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice. Focusing on neural network architectures without physics-informed input, we argue in favor of using an ansatz consisting of two decoupled real-valued networks, one for the amplitude and the other for the phase of the variational wavefunction. By introducing concrete mitigation strategies against inherent numerical instabilities in the stochastic reconfiguration algorithm we obtain a variational energy comparable to that reported recently with neural networks that incorporate knowledge about the physical system. Through a detailed analysis of the individual components of the algorithm, we conclude that the rugged nature of the energy landscape constitutes the major obstacle in finding a satisfactory approximation to the ground state wavefunction, and prevents learning the correct sign structure. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Point Neuron Learning: A New Physics-Informed Neural Network Architecture [8.545030794905584]
  This paper proposes a new physics-informed neural network architecture. It embeds the fundamental solution of the wave equation into the network architecture, enabling the learned model to strictly satisfy the wave equation. Compared to other PINN methods, our approach directly processes complex numbers and offers better interpretability and generalizability.
  arXiv  Detail & Related papers  (2024-08-30T02:07:13Z)
• Emergence of global receptive fields capturing multipartite quantum correlations [0.565473932498362]
  In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations. We show that monitoring the neural network weight space while learning quantum statistics allows to develop physical intuition about complex multipartite patterns. Our findings suggest a fresh look at constructing convolutional neural networks for processing data with non-local patterns.
  arXiv  Detail & Related papers  (2024-08-23T12:45:40Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation [5.283885355422517]
  We develop a novel architecture, Autoregressive NeuralNet, which bridges tensor networks and autoregressive neural networks. We show that Autoregressive NeuralNet parameterizes normalized wavefunctions, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.
  arXiv  Detail & Related papers  (2023-04-04T17:54:14Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Neural network enhanced measurement efficiency for molecular groundstates [63.36515347329037]
  We adapt common neural network models to learn complex groundstate wavefunctions for several molecular qubit Hamiltonians. We find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables.
  arXiv  Detail & Related papers  (2022-06-30T17:45:05Z)
• Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks [72.09574528342732]
  Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs) They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
  arXiv  Detail & Related papers  (2022-06-29T19:03:10Z)
• Learning topological defects formation with neural networks in a quantum phase transition [0.0]
  We investigate the time evolutions, universal statistics, and correlations of topological defects in a one-dimensional transverse-field quantum Ising model. We establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate, indicating a binomial distribution of the kinks. Finally, the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.
  arXiv  Detail & Related papers  (2022-04-14T06:00:19Z)
• Physical Constraint Embedded Neural Networks for inference and noise regulation [0.0]
  We present methods for embedding even--odd symmetries and conservation laws in neural networks. We demonstrate that it can accurately infer symmetries without prior knowledge. We highlight the noise resilient properties of physical constraint embedded neural networks.
  arXiv  Detail & Related papers  (2021-05-19T14:07:20Z)
• Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz [62.997667081978825]
  We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei. We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-28T14:52:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.